We start by providing motivation for the unconstrained Jacobians problem introduced in the main text. We will continue our proof using contradiction. Figure 1: Fully-connected ResNet34 (Type 1 model) trained on MNIST.Figure 2: Fully-connected ResNet34 (Type 1 model) trained on FashionMNIST. Figure 10: Fully-connected ResNet34 (Type 1 model) trained on MNIST. Figure 24: Fully-connected ResNet34 (Type 1 model) trained on MNIST.

All UK children could be offered screening for type 1 diabetes using a simple finger-prick blood test, say researchers who have been running a large study. Currently, many young people go undiagnosed and risk developing a life-threatening complication called diabetic ketoacidosis that needs urgent hospital treatment. Identifying diabetes earlier could help avoid this and mean treatments to control problematic blood sugar levels can be given sooner. Some 17,000 children aged three to 13 have already been checked as part of the ELSA (Early Surveillance for Autoimmune diabetes) study, funded by diabetes charities. Imogen, who is 12 and from the West Midlands, is one of those found to have diabetes thanks to the screening.

Electroencephalography (EEG) offers detailed access to neural dynamics but remains constrained by noise and trial-by-trial variability, limiting decoding performance in data-restricted or complex paradigms. Data augmentation is often employed to enhance feature representations, yet conventional uniform averaging overlooks differences in trial informativeness and can degrade representational quality. We introduce a weighted bootstrapping approach that prioritizes more reliable trials to generate higher-quality augmented samples. In a Sentence Evaluation paradigm, weights were computed from relative ERP differences and applied during probabilistic sampling and averaging. Across conditions, weighted bootstrapping improved decoding accuracy relative to unweighted (from 68.35% to 71.25% at best), demonstrating that emphasizing reliable trials strengthens representational quality. The results demonstrate that reliability-based augmentation yields more robust and discriminative EEG representations. The code is publicly available at https://github.com/lyricists/NeuroBootstrap.

Type 2 diabetes prevention and treatment can benefit from personalized lifestyle prescriptions. However, the delivery of personalized lifestyle medicine prescriptions is limited by the shortage of trained professionals and the variability in physicians' expertise. We propose an offline contextual bandit approach that learns individualized lifestyle prescriptions from the aggregated NHANES profiles of 119,555 participants by minimizing the Magni glucose risk-reward function. The model encodes patient status and generates lifestyle medicine prescriptions, which are trained using a mixed-action Soft Actor-Critic algorithm. The task is treated as a single-step contextual bandit. The model is validated against lifestyle medicine prescriptions issued by three certified physicians from Xiangya Hospital. These results demonstrate that offline mixed-action SAC can generate risk-aware lifestyle medicine prescriptions from cross-sectional NHANES data, warranting prospective clinical validation.

Vision-language models (VLMs) now rival human performance on many multimodal tasks, yet they still hallucinate objects or generate unsafe text. Current hallucination detectors, e.g., single-token linear probing (LP) and PTrue, typically analyze only the logit of the first generated token or just its highest-scoring component, overlooking richer signals embedded within earlier token distributions. We demonstrate that analyzing the complete sequence of early logits potentially provides substantially more diagnostic information. We emphasize that hallucinations may only emerge after several tokens, as subtle inconsistencies accumulate over time. By analyzing the Kullback-Leibler (KL) divergence between logits corresponding to hallucinated and non-hallucinated tokens, we underscore the importance of incorporating later-token logits to more accurately capture the reliability dynamics of VLMs. In response, we introduce Multi-Token Reliability Estimation (MTRE), a lightweight, white-box method that aggregates logits from the first ten tokens using multi-token log-likelihood ratios and self-attention. Despite the challenges posed by large vocabulary sizes and long logit sequences, MTRE remains efficient and tractable. Across MAD-Bench, MM-SafetyBench, MathVista, and four compositional-geometry benchmarks, MTRE achieves a 9.4% gain in accuracy and a 14.8% gain in AUROC over standard detection methods, establishing a new state of the art in hallucination detection for open-source VLMs.

From media platforms to chatbots, algorithms shape how people interact, learn, and discover information. Such interactions between users and an algorithm often unfold over multiple steps, during which strategic users can guide the algorithm to better align with their true interests by selectively engaging with content. However, users frequently exhibit inconsistent preferences: they may spend considerable time on content that offers little long-term value, inadvertently signaling that such content is desirable. Focusing on the user side, this raises a key question: what does it take for such users to align the algorithm with their true interests? To investigate these dynamics, we model the user's decision process as split between a rational system 2 that decides whether to engage and an impulsive system 1 that determines how long engagement lasts. We then study a multi-leader, single-follower extensive Stackelberg game, where users, specifically system 2, lead by committing to engagement strategies and the algorithm best-responds based on observed interactions. We define the burden of alignment as the minimum horizon over which users must optimize to effectively steer the algorithm. We show that a critical horizon exists: users who are sufficiently foresighted can achieve alignment, while those who are not are instead aligned to the algorithm's objective. This critical horizon can be long, imposing a substantial burden. However, even a small, costly signal (e.g., an extra click) can significantly reduce it. Overall, our framework explains how users with inconsistent preferences can align an engagement-driven algorithm with their interests in a Stackelberg equilibrium, highlighting both the challenges and potential remedies for achieving alignment.

C is the number of classes; and (RA4) top singular values of Residual Jacobians scale inversely with depth.

ABSTRACT In many IoT applications, the central interest lies not in individual sensor signals but in their differences, yet interpreting such differences requires expert knowledge. We propose DiffNator, a framework for structured explanations of differences between two time series. Using the Time-series Observations of Real-world IoT (TORI) dataset, we generate paired sequences and train a model that combine a time-series encoder with a frozen LLM to output JSON-formatted explanations. Experimental results show that DiffNator generates accurate difference explanations and substantially outperforms both a visual question answering (VQA) baseline and a retrieval method using a pre-trained time-series encoder. Index T erms-- Time series analysis, natural language generation, difference explanation, industrial IoT, large language model 1. INTRODUCTION The spread of the Internet of Things (IoT) has enabled large-scale collection of sensor data from industrial machinery.